Answer:
a) False
b) False
c) True
d) False
e) False
Step-by-step explanation:
a. A single vector by itself is linearly dependent. False
If v = 0 then the only scalar c such that cv = 0 is c = 0. Hence, 1vl is linearly independent. A set consisting of a single vector v is linearly dependent if and only if v = 0. Therefore, only a single zero vector is linearly dependent, while any set consisting of a single nonzero vector is linearly independent.
b. If H= Span{b1,....bp}, then {b1,...bp} is a basis for H. False
A sets forms a basis for vector space, only if it is linearly independent and spans the space. The fact that it is a spanning set alone is not sufficient enough to form a basis.
c. The columns of an invertible n × n matrix form a basis for Rⁿ. True
If a matrix is invertible, then its columns are linearly independent and every row has a pivot element. The columns, can therefore, form a basis for Rⁿ.
d. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. False
Row operations can not affect linear dependence among the columns of a matrix.
e. A basis is a spanning set that is as large as possible. False
A basis is not a large spanning set. A basis is the smallest spanning set.
Answer:
P(X = 17) = 0.3002
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
In this problem we have that:

We want P(X = 17). So


P(X = 17) = 0.3002
8ths are divided by 12.5 so 3 * 12.5 is 37.5
10ths are divided by 10 so 4 * 10 is 40
3/8 is < / = 4/10
Answer:
x^2-72=12x
Step-by-step explanation:
The given sequence is a geometric sequence. The property of geometric sequence is that each term is multiplied by a specific number known as "common ratio" to get the next term. In this case the common ratio is 1/2.
2 x 1/2 = 1
1 x 1/2 = 1/2
1/2 x 1/2 = 1/4
and so on..